Finite-Time Stability to Fractional Delay Cauchy Problem of Hilfer Type

Ahmed Salem; Rawia  Babusail; Moustafa El-Shahed; M. Eloasli

doi:10.37256/cm.4420232546

Authors

Ahmed Salem Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah, 21589, Saudi Arabia
Rawia Babusail Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah, 21589, Saudi Arabia
Moustafa El-Shahed 2Unaizah Faculty of Arts and Sciences, Qassim University, P.O. Box 3771, Unaizah, Qassim 51431, Saudi Arabia
M. Eloasli Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah, 21589, Saudi Arabia

DOI:

https://doi.org/10.37256/cm.4420232546

Keywords:

Hilfer derivative, fractional delay Cauchy problem, finite time stability, fractional delayed matrix cosine and sine

Abstract

The purpose of this work is to look at the solution’s representation for the non-homogeneous fractional timedelay Cauchy problem of Hilfer type in terms of the cosine and sine fractional delayed matrices of two parameters. The solutions are determined using the constant variation approach. Following that, finite-time stability under moderate circumstances is examined. At last, an example is offered to show how the theoretical results may be used.

Finite-Time Stability to Fractional Delay Cauchy Problem of Hilfer Type

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